Analytic Solutions for the Antigreenhouse Effect: Titan and the Early Earth

Abstract

The antigreenhouse effect results from a high altitude haze which blocks sunlight while allowing transmission of thermal infrared. An antigreenhouse is observed on Titan and has been proposed for the early Earth. Here, we derive an analytic solution useful for computing the atmospheric and surface temperature with both the greenhouse and antigreenhouse effects included. In agreement with detailed calculations, the analytic solution predicts that a runaway greenhouse on early Titan caused by accretional heat would collapse when the flux fell to 0.9 W m−2. For the present value of the solar luminosity a runaway greenhouse collapses at a geothermal heat flux of 0.4 W m−2. We show that the antigreenhouse effect may compromise attempts to solve the faint young sun problem on the early Earth with a methane–ammonia greenhouse shielded by an organic haze, more than doubling the infrared opacity needed to warm the early Earth compared to the case with no antigreen- house.